Locating a device that is moved in a three-dimensional space

ABSTRACT

A method of location of a device includes a displacement law containing a corrective factor of a bias combined by an arithmetical operation with a measured variable, and particles, each particle being associated with a current value of the corrective factor. The current value of the corrective factor being constructed at each iteration on the basis of a previous current value of the corrective factor, computed during a previous iteration, to which is added a random variable drawn according to a predefined probability law. The current values of various particles are initialized, before the first iteration, to various initial values, and during each iteration, for each particle whose coordinates are updated with the aid of this displacement law, the value of the corrective factor in the displacement law is taken equal to this corrective factor&#39;s current value associated with the particle.

RELATED APPLICATIONS

Under 35 USC 120, this application is a continuation of U.S. applicationSer. No. 14/741,818, filed Jun. 17, 2015, which claims the benefit ofthe Jun. 18, 2014 priority date of French Application FR 1455575, thecontents of which is herein incorporated by reference in their entirety.

FIELD OF INVENTION

The invention relates to locating a device as it is displaced inside athree-dimensional space.

BACKGROUND

It is often useful to locate a device that has been displaced within athree-dimensional space. This is particularly useful when the device isGPS inaccessible, as is often the case inside buildings or shoppingmalls.

Known methods of location rely on measurements provided by an inertialplatform housed within the device itself to measure the direction andamplitude of that device's displacement from a previous position. Amongthese known methods are those that use “particle filters” to estimatethe position of the device in the three-dimensional environment.Particle filters exploit the fact that there exist predefinedconstraints on the displacements of the device inside thethree-dimensional environment. A typical constraint might be that adisplacement cannot pass through a wall.

Under ideal conditions, known methods make it possible to preciselyestimate the position of the device. However, in reality, there mayexist a constant or systematic bias in the device's direction ofdisplacement and/or in the amplitude of the device's displacement inthat direction. This bias may have very different origins.

In some cases, a systematic bias arises from a bias in the measurementsof one or more sensors of the device's inertial platform. In othercases, a systematic bias arises from an error in modeling the relationthat links the measurements of the inertial platform to thedisplacement's direction or amplitude. Yet another source of suchsystematic bias is incorrect positioning of the device with respect toits direction of displacement.

If not corrected, a systematic bias degrades the precision of anestimate of the device's position. It is therefore desirable to correctit.

A difficulty that arises is that, to correct such a bias, it isnecessary to know its value. In most cases, this value is not known inadvance. Ideally, one should calibrate the device before using it. Thiswould enable it to determine its systematic bias. This value could thenbe used to correct forthcoming position estimates.

However, obliging the user to execute a prior calibration phase beforelaunching the location of the device is in most cases impractical. Tomake matters worse, in some cases, bias evolves over time. Thus, a userwould have to recalibrate the device from time-to-time.

SUMMARY OF INVENTION

The invention is aimed at avoiding this problem. In one aspect, theinvention features a method of precisely locating the device even in thepresence of a bias in a displacement's amplitude or direction.

One method features associating first particles with a first initialvalue for a corrective factor and associating second particles with asecond initial value for this same corrective factor.

To understand the benefit of this method, it is assumed that the firstinitial value is close to the actual value of the bias to be corrected.Conversely, it is assumed that the second initial value is further fromthe actual value of the bias to be corrected. Thus, the values of thecorrective factor that are associated with the first particles make itpossible to compensate the bias more correctly, and therefore toestimate the displacement of the device more precisely, on the basis ofthe same measurements.

The method of the invention features a variation of a procedure thatbegins with first and second steps. The first step is that of providinga map of the three-dimensional space and of predefined constraints onthe displacements of the device in this three-dimensional space. Thesecond step is that of using a computer to generate several distinctparticles. Each particle is associated with coordinates coding itsposition on the map. Each particle is also associated with a weight thatrepresents the probability that the device is situated at the site ofthis particle.

The method then continues with repeated execution of third, fourth, andfifth steps. For convenience, these steps will collectively be referredto as “the loop.”

The third step is that of receiving measurements representative of thedirection of displacement of the device and of the amplitude of thisdisplacement from its previous position. These measurements are carriedout by sensors onboard the displaced device. These sensors are realphysical structures that are not abstract in any way.

The fourth step is that of updating the coordinates of the position ofeach particle. This updating procedure is carried out as a function ofboth the measurements received during the third step and also of apredetermined displacement law for displacing this particle from itsprevious position P^(i) _(k-1) to a new position P^(i) _(k) in a mannercorrelated with the measured displacement of the device. Eachdisplacement law comprises at least a first measured variable whosevalue is dependent on the measurement of the direction of displacementreceived during the third step and a second measured variable whosevalue is dependent on the measurement of the amplitude of thisdisplacement received during the third step.

The fifth step includes making a decision as to whether a particle'sweight should be increased relative to those of other particles. Foreach particle, if the latest displacement of that particle from theposition P^(i) _(k-1) to the position P^(i) _(k) satisfies thepredefined constraints, the weight associated with that particle isincreased with respect to the weights of the particles whose latestdisplacement fails to comply with these predefined constraints.

After repetition of the loop, a sixth step includes estimating thedevice's position on the basis of the positions of the particles and ofthe weights associated with these particles. This estimation is carriedout, in part, by allotting more importance to the positions of theparticles associated with the highest weights.

In carrying out the foregoing procedure, there exists a tendency for theposition of the second particles to diverge further from the device'sreal position during the course of iterating the loop. Conversely, theposition of the first particles remains close to the real position ofthe device.

Consequently, it is probable that a displacement of a second particlewill rapidly violate one or more of the predefined constraints on thedisplacements in the three-dimensional environment. Hence, as iterationof the loop proceeds, the weight of the second particles rapidly becomesless important than that of the first particles. The determination ofthe device's position of the device is then carried out on the basis ofa certain number of iterations of the loop by giving more importance tothe positions of the first particles than to the positions of the secondparticles.

However, the positions of the first particles are obtained bycompensating the bias more correctly. Thus, an estimate of the device'sposition using the foregoing method rapidly becomes more precise than itwould have been had the bias not been corrected.

The foregoing method is a non-abstract method that results in animprovement in a particular technology, namely the technology of devicelocation. The nature of the improvement can be understood from arecitation of some of the advantages thereof.

A particular advantage of the method is that this increased precisioncomes with no need for prior calibration. In fact, as the loop'siteration proceeds, the corrective factor, which is what makes itpossible to more precisely compute a particle's position, is selectedautomatically. Since this corrective factor is arrived at more or lessconcurrently with estimating the device's position, the correctivefactor is also less likely to be out of date.

Among the advantages of the method described herein is that applying thecorrective factor to the measured variable corresponding to theamplitude of the displacement of the device makes it possible toautomatically correct a bias in the amplitude of the displacement ofthis device.

Also among the advantages is that applying the corrective factor to ameasured variable corresponding to the direction of the displacement ofthe device makes it possible to automatically correct a bias in thedirection of displacement.

Also among the advantages is that generating new particles and alsoassociating these new particles with initial values for the correctivefactor that are close to the corrective factor's current valuesassociated with the particles that have not been eliminated makes itpossible to increase the precision of the estimate of the value of thecorrective factor and therefore of the position of the device as theiteration of the loop proceeds.

Yet another advantage is that using, in the guise of predefinedconstraints, the existence of obstacles, which are impassable to thedevice in the three-dimensional environment, makes it possible toaccelerate the convergence of the location method of location toward aprecise estimate of the device's position.

Yet another advantage is that dividing the map into several zones andassociating, with each of these zones, a list of identifiers ofimpassable obstacles contained inside that zone makes it possible toretain a simple tiling of the map into several zones while being capableof using impassable obstacles situated entirely inside these zones.

Yet another advantage arises from dividing the map into several zonesand associating, with each of these zones, the displacement law thatmakes it possible to estimate the displacement of the device in thatzone with greater precision than would have been possible had anotherdisplacement law associated with another zone been used. This makes itpossible to increase the precision with which the device's position canbe estimated.

Yet another advantage arises from using a favored direction ofdisplacement in a zone of the map to change the weight associated with aparticle. This makes it possible to converge more rapidly toward aprecise estimate of the position of the device.

In some aspects, the invention further includes a non-transitoryinformation-recording medium that has, encoded thereon, instructions forthe execution of the above method of location when these instructionsare executed by an electronic computer in a non-abstract manner.

In yet another aspect, the invention features an electronic locatingunit configured to implement the foregoing method in a non-abstractmanner.

In another aspect, the invention features a device that is directlytransportable by a pedestrian who is moving through a three-dimensionalspace. Such a device is a non-abstract physical device that is made ofmatter and that includes an inertial platform able to measure physicalquantities representative of the direction of displacement of thisdevice and of the amplitude of this displacement and the electroniclocating-unit configured in the manner already described.

All methods and devices described herein are described in theirnon-abstract forms. Descriptions of abstract forms have been omitted.The claims are understood to cover only non-abstract subject matter. Asused herein, the term “non-abstract” is the converse of “abstract” asthat term has been interpreted by the U.S. Supreme Court and the FederalCircuit as of the priority date of this application.

The invention will be better understood on reading the description whichfollows, given solely by way of non-limiting example and while referringto the drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a vertical sectional schematic illustration of a buildinginside which is implemented a device-locating method;

FIG. 2 is a schematic illustration of a device for implementing thedevice-locating method;

FIG. 3 is a schematic illustration of a map used to locate the device ofFIG. 2 in the building of FIG. 1;

FIG. 4 is a flowchart of a device-locating method as implemented by thedevice of FIG. 2.

In these figures, the same references are used to designate the sameelements. Hereinafter in this description, the characteristics andfunctions that are well known to the person skilled in the art are notdescribed in detail.

DETAILED DESCRIPTION

FIG. 1 shows a multi-story building 2 inside of which a pedestrian 4walks freely. For ease of exposition, only a ground-floor story 6 and afirst story 8 are represented. Story-changing zones link storiestogether. Examples include a staircase or an elevator.

Each story comprises rooms and corridors delimited by walls that thepedestrian 4 cannot cross. The pedestrian 4 enters a room only bypassing through a door. A room's interior can also comprise obstaclesthat are impassable to the pedestrian 4. Examples of such obstaclesinclude pillars or other construction elements of the building 2.

A pedestrian 4 holds a device 10 while walking around the building 2.The device 10 locates itself on a map of the building 2 without recourseto sensors other than those that it comprises internally. In particular,the device 10 charts its position inside the building 2 without using anavigation system that calls upon external charting beacons implanted inthe environment of the building 2. These external beacons can besatellites or radio-wave emitters fixed to the building 2. Inparticular, the device 10 charts its position without recourse to a GPS(“Global Positioning System”).

FIG. 2 represents the device 10 in greater detail. The device 10comprises an electronic locating-unit 11 that comprises a memory 12 anda programmable electronic computer 14 capable of executing instructionsrecorded in the memory 12. The memory 12 comprises instructionsnecessary for executing the method of FIG. 4. In addition, the memory 12comprises a map 16 of the building 2. This map is described in greaterdetail with reference to FIG. 3.

The device 10 also comprises an inertial platform 17. The inertialplatform 17 uses a bus 19 to transmit data to the computer 14. This dataincludes measurements of the direction in which the device 10 is movingand of the amplitude of the displacement in this direction from thelatest logged position of this device 10. A typical inertial platform 17comprises a three-axis accelerometer 18, a gyrometer 19, and athree-axis magnetometer 20. In some embodiments, the inertial platform17 also comprises a barometer 21 for measuring the altitude of thedevice 10.

The device 10 also includes a screen 24 that makes it possible todisplay a graphical representation 26 of the map 16 on which a point PArepresenting the current position of the pedestrian 4 inside thebuilding 2. This point PA is therefore situated in the graphicalrepresentation 26 at the site of the map 16 corresponding to the currentposition of the device 10, and therefore, of the pedestrian 4.

In some embodiments, the device 10 is a smartphone or an electronictablet 2 programmed to execute the method of FIG. 4.

FIG. 3 graphically represents the content of the map 16 for the story 8of the building 2. What will now be described in respect of the story 8of the building 2 applies to each story of this building and to theground floor story 6.

The map 16 comprises several zones 30 . . . 35 that collectively tilethe entire story 8. In the illustrated embodiment, each zone is apolygon.

The zones are parallel to the story's floor and coplanar with a planereferred to herein as the “story plane.” The story plane is typicallyhorizontal.

The zones 30 . . . 35 are contiguous and non-overlapping zones. However,to increase the readability of FIG. 3, the zones 30 . . . 35 arerepresented as overlapping. Thus, each portion of the periphery of eachzone is common with at most one portion of the periphery of anotherdifferent zone.

In a typical implementation, the edges of each zone are at the site ofan obstacle that is impassable to the pedestrian 4 such as a wall.However, in some cases, one and the same zone can encompass severalrooms of the building 2. An example is the zone 33, which surrounds aroom 40 and another smaller room 42.

In FIG. 3, walls, which are shown as thin lines, delimit the peripheryof each room. Moreover, each room comprises at least one opening foraccessing the room's interior. In FIG. 3, the openings are between thewall ends marked by points. A typical opening is a door.

A zone can also encompass impassable obstacles in the room's interior.Examples of such impassable obstacles include an interior partition, apillar, or any other element of the building 2 that a pedestrian 4cannot cross. Zone 31, which comprises partitions 44, 46 situated insidea room 48, provides an example of such a zone.

For each polygonal zone, the map 16 contains an identifier for that zoneand the coordinates of the vertices of the polygon that defines thatzone. These coordinates are typically given in an XYZ frame.

The XYZ frame is an orthogonal frame in which the X and Y directions arehorizontal and the Z direction is vertical. In the illustratedembodiment, each zone is rectangular. As a result, it is possible toeconomize on memory by only storing the coordinates of a zone's twodiagonally opposite vertices.

For each zone, the map 16 also comprises a list of identifiers of justthe impassable obstacles situated inside that zone or on the peripheryof that zone and another identifier that identifies a law ofdisplacement within that zone. In some embodiments, the map alsoincludes a favored direction of displacement.

A horizontal segment contained in the plane of the floor codes theposition and the dimensions of each impassable object. Thus, eachobstacle identifier is associated with a pair of points E_(jd) andE_(jf). The points E_(jd) and E_(jf) mark, respectively, the start andthe end of a segment [E_(jd); E_(jf)], where j is the identifier of theimpassable obstacle. The coordinates of the points E_(jd) and E_(jf) inthe plane of the floor are known and contained in the map 16. In theillustrated embodiment, the zone 31 comprises eight obstacle identifiersIdO₁ . . . IdO₈. The identifiers IdO₁ to IdO₈ correspond, respectively,to the segments [E_(a); E_(b)]; [E_(b); E_(c)]; [E_(c); E_(d)]; [E_(d);E_(f)]; [E_(f), E_(g)]; [E_(h); E_(i)]; [E_(j); E_(R)] and [E_(p);E_(m)]. FIG. 3 illustrates the position of the points E_(a) to E_(m).

Each displacement law makes it possible to compute, on the basis of themeasurements of the inertial platform 17 at an instant t_(k), thedisplacement of a particle S^(i) from a previous position P^(i) _(k-1)to a new position P^(i) _(k). This displacement is directly correlatedwith that of the device 10. Typically, this displacement between thepositions P^(i) _(k-1) and P^(i) _(k) is identical or very close to thatof the device 10 between the instants t_(k-1) and t_(k). Subsequently,the superscript “i” is the identifier of the particle and the subscript“k” is the order number of the instant at which the direction and theamplitude of the displacement of the device 10 are measured.

The inertial platform 17 measures an angle θ_(k), in the plane of thestory, between the device's direction of displacement and the Xdirection. In some embodiments, the inertial platform 17 relies onmeasurements from the gyrometer 19 and from the magnetometer 20 toobtain such a measurement. The direction measured at the instant t_(k)will be referred to herein as “direction θ_(k)”.

The inertial platform 17 further provides a physical quantityrepresentative of the amplitude l_(k) of the displacement of the device10 in the direction θ_(k) between the instants t_(k-1) and t_(k). Forthis purpose, it is possible to integrate the measurement of theaccelerometer 18 between the instants t_(k-1) and t_(k) and, if themeasurement is zero, to retain the previous measured speed v_(k-1).

In the case of a pedestrian 4 walking on a horizontal floor, it ispossible to obtain a more precise estimate of the amplitude l_(k) byhaving the computer 14 detect, on the basis of the measurements providedby the accelerometer 18, the instant at which a pedestrian's footcontacts the floor. On the basis of these successive instants, thecomputer 14 computes a frequency f_(k) of the pedestrian's footsteps.

Next, the computer 14 computes an amplitude l_(k) of the pedestrian'sdisplacement in the direction θ_(k). It does so by using the followingfootstep model: l_(k)=Af_(k)+BT+C, where A, B, C and T are constantsthat are independent of the measurements of the inertial platform 17.The constants A, B, and C are independent of the pedestrian'smorphological characteristics. The constant T is equal to thepedestrian's height 4. By default, the constant T is the mean height ofa human being, for example 1.78 meters.

The device's speed v_(k) between the instants t_(k-1) and t_(k) isobtained by evaluating the expression: v_(k)=l_(k)/Δt, where Δt is theduration of the time interval between the instants t_(k-1) and t_(k).Typically, Δt is chosen equal to the duration between a pedestrian'sfootsteps.

Thus, when the pedestrian 4 moves by walking on the floor of the story8, a displacement law is given by the following relations:

x ^(i) _(k=) X ^(i) _(k-1) +v _(k) ·Δt·cos(θ_(k));

y ^(i) _(k) =y ^(i) _(k-1) +v _(k) ·Δt·sin(θ_(k))

where (x^(i) _(k), y^(i) _(k)) and (x^(i) _(k-1), y^(i) _(k-1)) are thecoordinates, in the plane of the floor, of the positions P^(i) _(k) andP^(i) _(k-1) of the particle S^(i).

In the case of a method of location of the device 10 implementing aparticle filter, it is beneficial to explore the largest possible numberof trajectories with the particles. Thus, the displacement of eachparticle is disturbed in a random manner. An example of a usabledisplacement law is the following:

x ^(i) _(k) =x ^(i) _(k-1) +v _(k) ·Δt·cos(θ_(k)+μ^(i) _(x));

y ^(i) _(k) =y ^(i) _(k-1) +v _(k) ·Δt·sin(θ_(k)+μ^(i) _(y));

where μ^(i) _(x) and μ^(i) _(y) are random variables.

At each instant t_(k) and for each particle S^(i), the values of therandom variables μ^(i) _(x) and μ^(i) _(y) are randomly drawn as afunction of a predefined centered probability distribution, i.e., onewith an expectation of zero. Thus, the mean of the values of each randomvariable μ^(i) _(x) and μ^(i) _(y) at the various successive instantst_(k) tends to zero as k increases.

In some embodiments, the predefined probability distribution is the samefor both random variables μ^(i) _(x) and μ^(i) _(y) and for all theparticles S^(i). Such a distribution, or “law,” is denoted Lp_(xy). Thisprobability distribution Lp_(xy) is characterized by a predeterminedstandard deviation σ_(xy). Embodiments include those in which theprobability distribution Lp_(xy) is a uniform distribution and those inwhich it is a Gaussian distribution.

In the illustrated embodiment, the standard deviation σ_(xy) is constantand independent of the measurements of the inertial platform 17 forupdating at each footstep. In some embodiments, the standard deviationσ_(xy) is greater than five centimeters. In others, it is greater thanten centimeters and, preferably, less than thirty-five centimeters.

In some cases, there also exists a direction bias. A direction bias is abias in the measurement of the direction θ_(k). A direction bias mayoriginate from a defect in the sensors of the inertial platform 17. Adirection bias can also arise from the pedestrian 4 having rotated thedevice 10 in a horizontal plane.

In some cases, there also exists a footstep bias. The footstep bias is abias in the measurement of the amplitude l_(k) of the device'sdisplacement. Like the direction bias, the footstep bias can originatefrom a defect in the sensors of the inertial platform 17. Or, thefootstep bias can originate from a modeling error and, in particular, anerror in the default value of the coefficient T in the footstep model.One source of footstep bias arises from not knowing the pedestrian'sactual height. Thus, a deviation in the pedestrian's height from averagehuman height of 1.78 meters introduces a systematic footstep bias in themeasurement of the amplitude l_(k).

Typically, these biases are constant at least over a time interval thatis long enough to be able to estimate them.

To compensate and correct for direction and footstep biases, thedisplacement law used integrates corrective factors α^(i) and ε^(i),associated with each particle S^(i). In one example, the displacementlaw is given by the following relations:

x ^(i) _(k) =x ^(i) _(k-1) +v _(k) ·Δt·(1+ε^(i) _(k))·cos(θ_(k)+α^(i)_(k))+μ^(i) _(x);

y ^(i) _(k) =y ^(i) _(k-1) +v _(k) ·Δt·(1+ε^(i) _(k))·sin(θ_(k)+α^(i)_(k))+μ^(i) _(y);

ε^(i) _(k)=ε^(i) _(k-1)+μ^(i) _(ε);

α^(i) _(k)=α^(i) _(k-1)+μ^(i) _(α);

where ε^(i) _(k) and ε^(i) _(k-1) are the values, respectively at theinstants t_(k) and t_(k-1), of the corrective factor ε^(i) used tocorrect the footstep bias, α^(i) _(k) and α^(i) _(k-1) are the values,respectively at the instants t_(k) and t_(k-1), of the corrective factorα^(i) used to correct the direction bias, and μ^(i) _(ε) and μ^(i) _(α)are random variables.

The random variables μ^(i) _(ε) and μ^(i) _(α) are used for the samereasons and in the same manner as the variables μ^(i) _(x) and μ^(i)_(y) introduced previously. Thus, a new value of the variables μ^(i)_(ε) and μ^(i) _(α) is randomly drawn at each new instant t_(k) and foreach particle S^(i) as a function, respectively, of a predefinedprobability distributions Lp_(ε) and of a predefined probabilitydistributions Lp_(α). Typically, these probability distributions Lp_(ε)and Lp_(α) are the same for all the particles S^(i). In the illustratedembodiment, the mathematical expectations of the probabilitydistributions Lp_(ε) and Lp_(α) are equal to zero. Consequently, just asfor the random variables μ^(i) _(x), and μ^(i) _(y), the mean of thevalues of each random variable μ^(i) _(ε) and μ^(i) _(α) at the varioussuccessive instants t_(k) tends to zero as k increases.

The variables μ^(i) _(ε) and μ^(i) _(α) only slightly disturb theprevious values ε^(i) _(k-1) and α^(i) _(k-1) of the corrective factorsε^(i) and α^(i). As a result the values of the corrective factors ε^(i)and α^(i) remain stable over time. For this purpose, the standarddeviations σ_(ε) and σ_(α), respectively, of the probabilitydistributions Lp_(ε) and Lp_(α) do not allow a fast variation of thevalues of the corrective factors ε^(i) and α^(i). As a result, it isdesirable to choose the standard deviation σ_(ε) to be small enough tokeep the ratio Σσ_(εk)/T to be less than ten percent per second and,preferably, less than five percent per second or one percent per second,where: σ_(εk) is the standard deviation of the distribution Lp_(ε)during the k^(th) iteration of an updating step 96, Σσ_(εk) is the sumof the standard deviations σ_(εk) between the q^(th) iteration and thep^(th) iteration of the updating step 96, where q is an integer that isless than p, and T is the duration, in seconds, of the time intervalwhich has elapsed between the q^(th) and the p^(th) iteration ofupdating step 96.

The updating step 96 is one in which the coordinates of the particleS^(i) are updated. This step is described in greater detail withreference to FIG. 4.

In the embodiment described herein the standard deviation σ_(ε) isconstant. Thus, the previous ratio can also be written: (p−q)σ_(ε)/T. Inthis case, whatever p and q might be, the ratio is constant. Thedifference p−q is generally large enough to cover a time period ofgreater than one second or four seconds and, generally, less than tenminutes or five minutes or one minute. For example, this differencebetween p and q is constant whatever p.

In a similar manner, the standard deviation σ_(α) is chosen to be smallenough to keep the ratio Σσ_(αk)/T less than ten degrees per second and,preferably, less than five degrees per second or one degree per second,where: σ_(αk) is the standard deviation of the probability distributionLp_(α) during the k^(th) iteration of the updating step 96, Σσ_(αk) isthe sum of the standard deviations σ_(αk) between the q^(th) iterationand the p^(th) iteration of the updating step 96, where q is an integerstrictly less than p, and T is the duration, in seconds, of the timeinterval that has elapsed between the q^(th) and the p^(th) iteration ofupdating step 96.

The standard deviation σ_(α) is also constant. Thus, the previous ratiocan also be written: (p−q)σ_(α)/T.

Just as for the variables μ^(i) _(x) and μ^(i) _(y), the variables μ^(i)_(ε) and μ^(i) _(α) make it possible to explore a large number ofpossible values for the corrective factors ε^(i) and α^(i).

The displacement law described hereinabove will be referred to herein asthe first displacement law. This first displacement law operates in mostsituations where the pedestrian 4 walks on horizontal ground.

On the other hand, in certain cases, there exist other, more precise,displacement laws.

For example, in a stairwell zone 35 that covers a stairwell comprising astaircase 50, the length of the pedestrian's footsteps depends on thedepth L_(m) of each step of the staircase 50. Thus, in the stairwellzone 35, it would be preferable to use a second displacement law thattakes this into account.

In some embodiment, a suitable second displacement law is identical tothe first displacement law except that the product v^(i)_(k)·Δt·(1+ε^(i) _(k)) is replaced with the measured variable n^(i)_(k). The variable n^(i) _(k) is given by the following relation: n^(i)_(k)=(Ent(|z^(i) _(k)−z^(i) _(k-1)|/H_(m)))·L_(m), where: z^(i) _(k-1)and z^(i) _(k) are the heights of the device 10 measured by the inertialplatform 17 at the instants t_(k-1) and t_(k), respectively, H_(m) isthe constant height of a stair of the staircase 50, L_(m) is the depthof a stair of the staircase 50, |z^(i) _(k)−z^(i) _(k-1)| is theabsolute value of the difference between z^(i) _(k) and z^(i) _(k-1),and Ent (. . . ) is a function that returns the integer part of itsargument. The height H_(m) and the depth L_(m) are known in advance andrecorded in the map 16. The values of the measured variables z_(k) andz_(k-1) are obtained, typically, on the basis of the measurements by thebarometer 21. In this case, only the stairwell zone 35 relies on thesecond displacement law. All the other zones of the story 8 remainassociated with the first displacement law.

Within the building 2, there exist zones 30, 31, 33 and 34 in which apedestrian 4 moves freely in all directions. Stated otherwise, withinthese zones, all displacement directions are equally probable. In thisparticular example, the zones have no favored direction of displacement.

Conversely, there also exist zones of the building 2 in which not alldisplacement directions are equally probable.

For example, a corridor zone 32 spans a long corridor parallel to the Xdirection. In this corridor zone 32, a pedestrian's most probabledisplacement would be parallel to the X direction. In fact, it would berather improbable for the pedestrian 4 to move transversely to thecorridor's longitudinal direction. In this case, there is said to be afavored displacement direction in the corridor zone 32.

Each favored direction is coded by an angle y in the plane of the floorbetween this favored direction and the X direction. Moreover, in thisembodiment, an angular tolerance σ_(γ) is also associated with eachfavored direction. This angular tolerance is generally expressed indegrees or in radians. For example, in the case of the corridor zone 32,the angle γ is equal to zero degrees and the angular tolerance σ_(γ) is±30°. In the embodiment described here, the stairwell zone 35 is alsoassociated with a favored direction for ascending and descending thestaircase 50. For this favored direction, the angle γ is equal to ninetydegrees and the angular tolerance σ_(γ) is equal to ±20°.

Referring now to FIG. 4, the device 10 begins the process of locatingitself within a building 2 by having the unit 11 implement a locationalgorithm. This location algorithm is referred to herein as a “particlefilter.”

The method's first step 90 occurs upon triggering the locationalgorithm. This might occur, for example, when a pedestrian 4 interactswith the device's user interface.

The computer 14 begins by generating an initial assembly of N₀ particlesS^(i), where i is an identifier of the particle making it possible todistinguish it from among the set of other particles generated. Thenumber N₀ of particles S^(i) depends on the initial knowledge that onehas about the position of the device 10 in the building 2 and the areaof the building. Typically, N₀ is greater than ten or a hundred and lessthan five thousand or one thousand.

Each particle S^(i) is initially associated with an initial positionP^(i) ₀ inside the building 2. The position P^(i) ₀ comprises thecoordinates x^(i) ₀, y^(i) ₀ and z^(i) ₀ of the particle S^(i) in theXYZ frame, with an initial value w^(i) ₀ of the weight w^(i)representing the probability that the device 10 is situated at the siteof this particle S^(i) at the instant t₀, with an initial value of α^(i)₀ for the corrective factor α^(i), and with an initial value of ε^(i) ₀for the corrective factor ε^(i).

The first step 90 also include initializing the initial position P^(i) ₀and the variables w^(i) ₀, α^(i) ₀, and ε^(i) ₀ with their respectiveinitial values. Numerous methods for initializing the positions P^(i) ₀and the weights w^(i) ₀ of each particle are possible. For example, ifthe initial position of the device 10 is known to within one meter, thepositions P^(i) ₀ of all the particles S^(i) are drawn at random insidea circle centered on the known position and having a one-meter radius.It is also possible to set each weight w^(i) ₀ to be equal to 1/N₀,where N₀ is the initial number of particles generated.

Each value α^(i) ₀ is drawn at random in such a way that thedistribution of the initial values α^(i) ₀ follows a predeterminedprobability distribution Lp_(α0), such as a uniform distribution, aGaussian distribution, or some other distribution. The probabilitydistribution Lp_(α0) is generally not the same as the probabilitydistribution Lp_(α) that is used to obtain the values of the randomvariable μ^(i) _(α).

The a priori knowledge that one has about the distribution of thedirection bias makes it possible to choose the probability law for theinitial values α^(i) ₀ that most resembles the one observed. It is alsothis a priori knowledge that makes it possible to fix the value of thestandard deviation σ_(α0) of the distribution Lp_(α0).

In some embodiments, the standard deviation σ_(α0) is chosen to be equalto 360° if one has no information about the direction bias. In otherembodiments, the standard deviation σ_(α0) is chosen to be less than 45°if one has only limited information about the direction bias. Aparticular property of the probability distribution Lp_(α0) is that itdoes not necessarily have a zero mean.

Each initial value ε^(i) ₀ is chosen as described previously for theinitial values α^(i) ₀ except that a predefined probability distributionLp_(ε0) is used for the footstep bias instead of the distributionLp_(α0). Moreover, the probability distribution Lp_(ε0) is notnecessarily identical to the distribution Lp_(α0). Indeed, generally,the direction bias and footstep bias are not correlated.

Typically, the standard deviation σ_(ε0) of the distribution Lp_(ε0) isequal to 30%±5% if one has no information about the footstep bias. Insome embodiments, the standard deviation σ_(ε0) is chosen to be lessthan 20% if one has only a little information about the footstep bias.

During a second step 92, the inertial platform 17 transmits itsmeasurements to the computer 14. After having received thesemeasurements, the computer 14 uses them to compute the speed v_(k) andthe angle θ_(k) of the current displacement of the device 10 from itslatest position. The new measurements of the speed v_(k) and of theangle θ_(k) are computed each time that the computer 14 detects that thepedestrian's foot has just touched the floor.

During a third step 94, the computer 14 identifies, for each particleS^(i), the zone inside which that particle is currently situated. Insome embodiments, for each particle S^(i), the computer 14 compares itslast-known position P^(i) _(k-1) with the periphery of each zone of themap 16.

For example, in the case of rectangular zones aligned with the XYZframe, the computer 14 tests whether the following two inequalities aresatisfied: x_(Aj)≤x^(i) _(k-1)≤x_(Bj) and y_(Aj)≤y ^(i) _(k-1)≤y_(Bj),where: the subscript j is an identifier of the zone of the map 16 makingit possible to distinguish it from the other zones, x_(Aj) and y_(Aj)are the coordinates of that vertex of zone j which is closest to theorigin of the XYZ frame, and x_(Bj) and y_(Bj) are the coordinates ofthat vertex of zone j that is furthest from the origin of the XYZ frame.

If these two inequalities are satisfied, then the particle S^(i) belongsto zone j. Preferably, the computer 14 first tests whether the particleS^(i) has remained in the same zone. A finding that the particle S^(i)does not belong to any zone triggers additional processing. In somecases, such a finding causes the computer 14 to eliminate that particle.

During the fourth step 96, once the zone to which each particle S^(i)belongs has been identified, each particle is displaced in a mannercorrelated with the measured displacement of the device 10 from itsprevious position P^(i) _(k-1) up to a new position P^(i) _(k).Accordingly, the coordinates of each particle S^(i) are updated as afunction of three variables, namely: the latest measurements receivedfrom the inertial platform 17, the coordinates of the previous positionP^(i) _(k-1) of this particle, and the displacement law associated withthe zone inside which the particle S^(i) is situated. For this reason,the fourth step 96 is often called an “updating step.”

The displacement law to be used is therefore that associated with thezone identified during the third step 94.

For example, if the particle S^(i) is situated inside one of the zones30 . . . 34, then the coordinates of the new position P^(i) _(k) areestablished using the first displacement law. On the other hand, if theparticle S^(i) is situated inside the zone 35, then the coordinates ofthe new position P^(i) _(k) are established using the seconddisplacement law.

At each new execution of the updating step 96, the new values for thevariables μ^(i) _(x), μ^(i) _(y), μ^(i) _(α) and μ^(i) _(ε) are randomlydrawn with the aid of the laws Lp_(xy), Lp_(α) and Lp_(ε), respectively.

During a fifth step 98, the computer 14 updates the weights w^(i) ofeach particle S^(i). More precisely, the computer 14 decreases theweight w^(i) of the particle S^(i) if its latest displacement from theposition P^(i) _(k-1) to the position P^(i) _(k) is inconsistent withpredefined constraints associated with the zone inside which it issituated.

Typically, for each particle S^(i), the computer 14 verifies that firstand second constraints have been met. The first constraint is that thesegment [P^(i) _(k-1); P^(i) _(k)] must not cross an impassable obstacleof the zone inside which the particle S^(i) is situated. The secondconstraint is that the displacement direction from the position P^(i)_(k-1) to the position P^(i) _(k) complies with the favored displacementdirection associated with the zone inside which the particle S^(i) issituated.

In some embodiments, a constraint on the displacement of the particleS^(i) is defined as being a condition that, if satisfied by the particleS^(i), increases the weight w^(i) of that particle S^(i) with respect tothe weight of the particles that do not satisfy this condition.Conversely, if this condition is not satisfied by the particle S_(i),then the condition decreases the weight w^(i) of the particle S^(i)relative to the weights of the particles that did satisfy the condition.

To evaluate the first constraint, for each particle S^(i), the computer14 searches for whether there exists an intersection between the segment[P^(i) _(k-1); P^(i) _(k)] and each impassable obstacle of the zoneinside which the particle is situated. This zone was identified duringthird step 94. This intersection search is carried out solely with theimpassable obstacles whose identifiers are contained in the listassociated with the identified zone. Since each obstacle is coded by asegment, this intersection search amounts to a search for anintersection between two segments.

If an intersection exists, then a very low value or a value of zero isassigned to the weight w^(i). An example of a very low value is a valueless than 0.2 or 0.1. In the converse case, the value of the weightw^(i) remains unchanged.

If the zone inside which the particle S^(i) is situated is notassociated with a favored direction, then the second constraint is notused to update the weight w^(i). In the converse case, the secondconstraint is used.

To evaluate the second constraint, the computer 14 computes a weightw^(i) _(θ) on the basis of the deviation between the measured directionθ_(k) for the displacement of the particle S^(i) and the favoreddirection of the zone inside which it is situated. The value of theweight w^(i) _(θ) grows larger as the angular deviation between thefavored direction γ and the direction of displacement from the positionP^(i) _(k-1) to P^(i) _(k) grow smaller. The value of the weight w^(i)_(θ) is established while taking account of the tolerance σ_(y)associated with this favored direction. The value of the weight w^(i)_(θ) is therefore larger if the angular deviation between the directionof displacement of the particle S^(i) and the favored direction lies inthe tolerance margin defined by the value of σ_(γ) and, in the conversecase, the value of the weight w^(i) _(σ) is smaller.

In some embodiments, the value of the weight w^(i) _(σ) is computed withthe following relation: w^(i) _(σ)=p·exp[(θ_(k)+α^(i) _(k)−γ)²/(2σ_(γ)²)], where p is a predefined constant coefficient. The value α^(i) _(k)of the corrective factor α^(i) of the direction bias is also used tocompute this weight w^(i) _(σ).

Thereafter, the value of the weight w^(i) is set equal to its previousvalue multiplied by the value of the weight w^(i) _(θ) thus obtained.

During a sixth step 100, the computer 14 normalizes the weights w^(i) ofall the particles S^(i) so that the sum of all these weights is equal tounity. In some embodiments, the computer 14 computes the sum W of allthe weights w^(i) and then divides each weight w^(i) by the sum W.

During a seventh step 102, which is a resampling step, the computer 14re-samples the particles S^(i). The seventh step 102 includeseliminating those particles whose weights w^(i) have become too low toreplace them with particles associated with parameters whose weights arehigher.

Numerous re-sampling techniques are known. For example, here, we applythe SIR (Sequential Importance Resampling) scheme described in thefollowing book: B. Ristic, S. Arulampalam, N. Gordon, “Beyond the KalmanFilter, particle filter for tracking applications,” Artech House, 2004.

The re-sampling scheme includes classifying the particles into twogroups: the particles to be regenerated and the surviving particles. Theparticles to be regenerated are those whose weight is below apredetermined threshold. All other particles are surviving particles.

Thereafter, for each particle to be regenerated, the computer 14eliminates the old particle and then generates a new particle to replaceit. To generate a new particle, the computer 14 randomly draws aparticle from the group of surviving particles. This random drawing iscarried out preferably in such a way that the probability of being drawnis proportional to the weight of the surviving particle.

Thereafter, the drawn surviving-particle's position P^(i) _(k) and itsvalues α^(i) _(k) and ε^(i) _(k) are assigned to the newly-generatedparticle. During this step, the computer 14 adds a random disturbance tothe position and to the values of the corrective factors. In someembodiments, it does so by using the random variables μ_(x), μ_(y),μ_(α) and μ_(ε). However, these disturbances are calibrated in such away that the values α^(i) _(k) and ε^(i) _(k) assigned to the generatedparticle remain close to the current values for the corrective factorsassociated with the recently drawn surviving-particle. Typically, themean of the values α^(i) _(k) that are assigned to the generatedparticles are closer to the mean of the values α^(i) _(k) of thesurviving particles than to the mean of the values α^(i) _(k) of theeliminated particles. The same holds for the values ε^(i) _(k) assignedto the generated particles.

A new weight is also assigned to each generated particle and,optionally, to the surviving particle from which it arises.

During an eighth step 104, the computer 14 estimates the position PA ofthe device 10 on the basis of the positions P^(i) _(k) and of theweights w^(i) of all the particles S^(i). Numerous schemes are possiblefor doing this. For example, the position PA is taken equal to that ofthe particle S^(i) having the highest weight w^(i). In anotherembodiment, the position PA is taken equal to the mean of the positionsP^(i) _(k) of the particles S^(i) on weighting each position P^(i) _(k)by the weight w^(i). Another scheme is also described in application WO2012158441.

Finally, during a ninth step 106, a point is displayed at the positionPA on the graphical representation 26 of the map 16 to indicate to thepedestrian 4 his position on this map and therefore his position insidethe building 2.

The steps between the second step 92 and the ninth step 106 inclusivedefine a loop that repeatedly executes. As these iterations proceed, theprecision of the estimate of the position of the device 10 increases. Itdoes so because only the most probable positions P^(i) _(k) areretained.

In parallel with the eighth step 104, during a tenth step 108, thecomputer 14 computes an estimate E_(α) 0 of the direction bias and anestimate E_(ε) of the footstep bias on the basis, respectively, of thecurrent values α^(i) _(k) and ε^(i) _(k) of the particles S^(i). In someembodiments, the estimate E_(α) is set equal to the mean of the currentvalues α^(i) _(k) of all the particles S^(i). In a similar manner, thevalue of the estimate E_(ε) is set equal equal to the mean of thecurrent values ε^(i) _(k) of all the particles S^(i).

The precision of the estimates E_(α) and E_(ε) increases as therepetitions of the loop proceed. Indeed, it is probable that theparticle S^(i) associated with an incorrect current value for thecorrective factor α^(i) or ε^(i) will rapidly fall out of compliancewith the constraints that were evaluated during a fifth step 98. Hence,the particles S^(i) associated with incorrect current values for thecorrective factors are preferably eliminated during the seventh step102. Thus, as the loop iterates, the particles S^(i) associated withcorrect current values for the corrective factors are preferentiallyselected as surviving particles during the seventh step 102. Hence, theestimates E_(α) and E_(ε) converge toward the actual values of thedirection bias and the footstep bias.

Moreover, since the values of the corrective factors α^(i) and ε^(i)converge toward the actual values of the direction and footstep biasesas the loop iterates, the corrective factors correct these direction andfootstep biases with increasing precision. Hence, the presence of thesecorrective factors in the displacement law makes it possible tosubstantially increase the precision of the estimate of the position PAeven in the presence of such direction and footstep biases.

The estimates E_(ε) and E_(α) can be displayed on the screen 24 or usedby other applications to correct the direction and footstep biases.

Numerous other embodiments are possible.

For example, some embodiments feature sensors that provide a mean valueof the variable measured at an instant k as well as a standard deviationin that measurement. In this case, the measured values of the angleθ_(k) and of the amplitude l_(k) are obtained by drawing the values atrandom using a Gaussian probability distribution whose mean and standarddeviation are equal to those transmitted by the sensors. This makes itpossible to take measurement noise into account.

Embodiments include those in which the pedestrian 4 carries the device10 and those in which the pedestrian pushes a trolley on which thedevice 10 has been mounted.

The latter case includes embodiments that measure speed v_(k) byintegrating the acceleration measured by the trolley and those thatestimate speed by detecting detect a frequency of the impacts that occureach time a wheel of the trolley rolls over a joint between regularinterruptions on pavement, such as in the interruption betweenflagstones or paving stones.

In some embodiments, a motorized robot transports the device 10 withoutthe aid of the pedestrian 4. In this case, the amplitude of thedisplacement can be measured by measuring the number of wheelrevolutions of a driving wheel of the robot.

The method described above applies to any type of three-dimensionalspace in which the device 10 can be displaced. The space can also besituated outdoors and outside any building. In either case, this methodis useful for locating a person in a place where location by GPS or onthe basis of telephonic relay is impossible.

Other ways of coding the constraints on the displacement of the device10 are usable in the above method.

In some practices, rather than recording the position of the walls, itis possible to record all the possible paths. If the displacement of aparticle does not follow one of these possible paths, then its weight isdecreased.

Yet other practices feature recording the position of the doors ratherthan the walls. In such cases, the weight of a particle is increased ifit the latter goes from one room to another by passing through a door.

Still other practices use different predefined constraints to update thevalue of the weight w^(i).

In some cases, there exists other information that provides anapproximate measurement of the device's position. Such cases would theninclude increasing the weight w^(i) if the position P^(i) _(k) is closeto this approximate position and decreasing the weight if if theposition P^(i) _(k) is far from this approximate position. Sources ofsuch other information include power received by the device 10 from aradio source of known output power having a known position in the XYZframe. A common example of such a radio source is a Wi-Fi terminal.

Although a constraint against collision of a particle with an impassableobstacle is, in practice, most common, it is not absolutely necessary ifthere exist other predefined constraints such as those described abovethat can be used.

Some embodiments omit the sixth step 100 of normalizing the weight w^(i)of the particles S^(i).

During the re-sampling of the particles, numerous other algorithms fordetermining the initial position of the regenerated particles can beused instead of that described above. A suitable algorithm is theKullbak-Leibler-Divergence algorithm.

Other algorithms are possible for associating a new current value α^(i)_(k) and ε^(i) _(k) with each regenerated particle. Each new value α^(i)_(k) is dependent on one or more of the values α^(i) _(k) associatedwith the particles that have not been eliminated and is independent ofthe values α^(i) _(k) associated with the particles that have beeneliminated. The same holds for the new value ε^(i) _(k).

Another simplified practice omits the seventh step 102. Even withoutre-sampling, the method described herein makes it possible to increasethe precision with which one can located the device's position. This isbecause the weight w^(i) of each particle S^(i) associated with anincorrect current value α^(i) _(k) or ε^(i) _(k) decreases as the loopiterates.

Other schemes for determining whether a particle is situated inside azone are possible.

Practices further include those in which the zones have shapes otherthan polygons. Examples of such practices include those in which thezone is circular. In such cases, the map 16 records the circle's centerand radius. In fact, there are no limitations on the zone's shape otherthan the requirement that the coordinates of its periphery bedeterminable in the in the XYZ frame.

In the foregoing method, each zone is associated at one and the sametime with impassable-obstacle identifiers, a displacement law, and afavored direction.

In an alternative practice, several immediately contiguous zones sharethe same displacement law.

For example, in the illustrated embodiment the zones 30 . . . 34 are allassociated with the first displacement law. In this case, it may be morebeneficial to record, in the map 16, several stacked strata of zones forthe same story.

Each stratum in the resulting set of stacked strata comprises at leastone zone and, typically, a set of several zones covering the entire areaof the floor. The zones of one stratum are distinguished from the zonesof another stratum by the type of property that it associates with thosezones.

In one example, a first stratum comprises zones that are associated withimpassable-obstacle identifiers. A second stratum comprises zones thatare associated only with a respective displacement law. Finally, a thirdstratum comprises zones that are associated solely with a favoreddirection.

When such a stack of strata is applied to the story 8, the zones of thefirst stratum are, for example, identical to the zones 30 to 35 exceptthat they comprise only the identifiers of impassable obstacles.

In the illustrated embodiment, the second stratum is limited to twozones. One of them is identical to the zone 35 except that it is solelyassociated with the second displacement law. The second stratum'sremaining zone corresponds to the union of zones 30 to 34 and is solelyassociated with the first displacement law.

The third stratum comprises four zones, the first and second beingidentical, respectively, to zones 32 and 35 except that they are solelyassociated with a respective favored direction. The third zonecorresponds to the union of zones 30 and 31 and the fourth zone thencorresponds to the union of zones 33 and 34, which are not associatedwith any favored direction.

A location method that relies on a map comprising several strata isidentical to that described above except that, for each particle S^(i),the zone of each stratum inside which it is situated is identified.Thereafter, it is these zones inside which it is situated that make itpossible to identify the displacement law to be used and the predefinedconstraints to be tested so as to update the value of its weight w^(i).The use of several strata of zones may simplify the definition of thesezones.

In other practices, one of these strata corresponds to an accessibilitymap. Among these are practices in which the accessibility map hascontiguous boxes. Among these are practices in which the contiguousboxes that are associated with the same value of the degree Λ ofaccessibility are grouped together within one and the same zone.

Each zone can also be associated with additional predefined constraintsfor updating the weight w^(i) of the particles situated in that zone.For example, some practices include associating, with each zone, acoefficient w_(α) of accessibility that represents the probability thata pedestrian will enter this zone. Thereafter, when updating the weightw^(i) of a particle S^(i) situated in this zone, the weight w^(i) is setto be equal to its previous value multiplied by this coefficient w_(α).

Other displacement laws are usable.

In some practices, the standard deviations σ_(α) and σ_(ε) are notconstant. Among these are practices in which they are constant over longdurations and then modified for a brief time interval before returningto their previous values. For example, solely during this brief timeinterval, the ratios Σσ_(εk)/T and/or Σσ_(αk)/T are permitted to exceedthe previously defined thresholds.

Typically, the temporary increase of the values of the standarddeviations σ_(α) and σ_(ε) is used to reinitialize the current valuesα^(i) _(k) and ε^(i) _(k). Generally, the values of the standarddeviations σ_(α) and σ_(ε) are constant for more than 90% of the timethat the device 10 is being used. This prevents a rapid variation of thevalues of the corrective factors ε^(i) and α^(i) during that 90% of thetime.

Some practices include verifying that the ratio Σσ_(εk)/T is maintainedbelow a predetermined threshold over at least 90% of the time that thedevice 10 is being used. Among these practices are those that includesetting the difference p-q equal to a constant. Thereafter, the ratioΣσ_(εk)/T is computed for each value of p corresponding to an iterationof the updating step 96 occurring during this time of use. If at least90% of the ratios thus computed are below the predetermined threshold,then one can infer that the ratio is being maintained below thispredetermined threshold for more than 90% of the time that the device 10is being used. The same computation can be used for the ratio Σσ_(αk)/T.The time of use is, for example, a period of continuous use of thedevice 10 without stopping the execution of the method of FIG. 4.

In other practices, the expectation of one of the probabilitydistributions Lp_(ε) or Lp_(α) is non-zero. This introduces anadditional bias that is added to the real bias. The current values ε^(i)_(k) or α^(i) _(k) can also be computed on the basis of a previous valueother than ε^(i) _(k-1) or α^(i) _(k-1). For example, ε^(i) _(k) iscomputed on the basis of the previous value ε^(i) _(k-n), where n is aninteger greater than one. Thus, it is also possible to use the followingrelations to compute the current value of ε^(i) _(k): ε^(i) _(k)=(ε^(i)_(k-1)+ε^(i) _(k-2))/2+μ^(i) _(ε) or ε^(i) _(k)=ε^(i) _(k-2)+μ^(i) _(ε).The same thing applies to the computation of the current value α^(i)_(k).

Moreover, if it is known that the direction bias is zero or negligible,then the first and the second displacement laws are simplified byeliminating the corrective factor α^(i). Conversely, if it is known thatthe footstep bias is zero or negligible, then the first displacement lawis simplified by eliminating the corrective factor ε^(i). The correctivefactor remaining in the first displacement law is thereafter estimatedas described above with reference to FIG. 4. Conversely, it is possibleto add additional corrective factors to the first displacement law. Forexample, if the best possible value of the coefficient A in the footstepmodel of the first displacement law is not known precisely, it is thenpossible to use the following footstep model l_(k)=πAf_(k)+BT+C, where πis an additional corrective factor. The value of the factor π is thenestimated in the same manner as was described for the corrective factorsα^(i) and ε^(i). It will be noted that in the case of the correctivefactor π, the latter is a multiplicative factor and not a subtractivefactor, that is to say that it multiplies the measured variable f_(k).

Displacement laws other than those described above may be used. Forexample, a displacement law specifically adapted to the displacement onan escalator or on a moving walkway or in an elevator can readily bedesigned and associated with the zone comprising this escalator, thismoving walkway or this elevator. Moreover, if there exists a measurementbias in these particular zones, then it is desirable to introduce acorrective factor into the displacement law to compensate thismeasurement bias. If, initially, the value of this corrective factor isnot known, then this value is estimated in the same manner as wasdescribed for the corrective factors α^(i) and ε^(i).

Neither the ninth step 106 nor the tenth 108 need be carried out aftereach iteration of the loop. In some practices, these steps are carriedout only after completion of every other iteration.

The previous embodiments have been described in the particular casewhere all processing steps to determine the position PA are carried outby the computer 14 of the device 10.

Alternative practices distribute these processing steps among severaldistinct computers. In some practices, these distinct computers includea computer server that is mechanically independent of the device 10.Among these practices are those in which the device 10 transmits themeasurements to such a server, which then determines the position PA andreturns it to the device 10, which then displays it on its screen 24.Among these practices are those that also include recording the map 16in the server's memory.

Yet other practices include selecting a specific displacement law as afunction of the zone in which the particle is situated in a manner thatis independent of the other characteristics of the method of FIG. 4.Among these are practices that include selecting the displacement lawindependently of the use of corrective factors such as the factors α^(i)and ε^(i) and/or independently of the use, in the guise of predefinedconstraints, of the favored displacement directions.

Likewise, the use of favored directions of displacement associated withzones can also be implemented independently of the other characteristicsof the method of FIG. 4. In particular, the use, in the guise ofpredefined constraints, of the favored directions of displacement can beimplemented independently of the use of corrective factors such as thefactors α^(i) and ε^(i) and/or independently of the selection of thedisplacement law as a function of the zone inside which the particle issituated.

Having described the invention and a preferred embodiment thereof, whatis claimed as new and secured by letters patent is:

1. A method comprising making an improvement in the technical field oflocating a device, wherein said improvement is the ability to locatesaid device in the absence of a GPS signal, wherein said methodcomprises locating said device, said device having been displaced insidea three-dimensional space, wherein an inertial platform is mounted onsaid device such that said inertial platform is on-board said device,wherein said inertial platform is configured for providing a measurementof a physical quantity representative of displacement of said device,wherein said inertial platform comprises a sensor system, wherein saidsensor system comprises sensors, wherein said sensors comprise anaccelerometer, wherein an information transmission bus connects saidinertial platform to a computer that detects, on the basis ofmeasurements provided by the accelerometer through the informationtransmission bus, movement of said inertial platform, said movementbeing indicative of said displacement of said device, wherein saidcomputer further comprises a memory that contains, stored therein, a mapand instructions for execution by said computer, wherein said methodcomprises executing a first step, executing a second step, andrepeatedly executing a sequence of steps that comprises a third step, afourth step, and a fifth step, wherein the first step comprisesproviding a map of the three-dimensional space and of predefinedconstraints on the displacements of the device in the three-dimensionalspace, wherein the second step comprises using said computer to generateseveral distinct particles, wherein each particle is associated withcoordinates and with a weight, said coordinates coding the particle'sposition on the map, and the weight representing the probability thatthe device is situated at the site of the particle, wherein the thirdstep comprises receiving measurements representative of the direction ofdisplacement of the device and of the amplitude of the displacement ofthe device from a previous position thereof, the measurements beingcarried out by said sensors, wherein the fourth step comprises, for eachparticle, updating the coordinates of the position of the particle as afunction of the measurements received during the third step and of apredetermined displacement law for displacing the particle from aprevious position thereof to a new position thereof in a mannercorrelated with the measured displacement of the device, wherein thefifth step comprises, for each particle, when the latest displacement ofthe particle from the previous position to the new position satisfiesthe predefined constraints, increasing the weight associated with theparticle relative to weights of the particles whose most recentdisplacement does not satisfy the predefined constraints,—estimating theposition of the device on the basis of the positions of the particlesand of the weights associated with these particles by allotting, duringthe estimation, more importance to the positions of the particlesassociated with the highest weights, wherein the map contains severaldistinct zones, each distinct zone being associated with coordinatesdefining the position on the map of a periphery of the zone and with apredetermined displacement law, wherein at least two of the severaldistinct zones are associated with different predetermined displacementlaws, wherein the predetermined displacement law is selected from amonga set of several different displacement laws because the predetermineddisplacement law makes it possible to estimate, more precisely,—on thebasis of the same measurements received, the direction and the amplitudeof the displacement of the device when the device is situated inside thezone than would be possible if any one of the other displacement law ofthe set of several different displacement laws were used, wherein thedisplacement laws from the set of several different displacement lawsare distinguished from one another by mathematical operations that linkthe coordinates of a particle to the measurements received during thethird step, and wherein the fourth step comprises, for each particle,identifying the zone inside which the particle is situated by comparingthe coordinates of the particle with the peripheries of the zones of themap as defined by the coordinates provided during the first step, andthe coordinates of the particle updating using just the predetermineddisplacement law associated with the zone identified during theidentification operation.
 2. The method of claim 1, wherein thepredetermined displacement law comprises at least one first measuredvariable whose value is dependent on the measurement of the direction ofdisplacement received during the third step, a second measured variablewhose value is dependent on the measurement of the amplitude of thedisplacement received during the third step, and a corrective factor tocorrect for a bias, the corrective factor to be combined by anarithmetical operation with one of the measured variables, and whereineach particle is associated with a current value of the correctivefactor, the current value of the corrective factor being constructed ateach iteration of the fourth step on the basis of a previous value ofthe corrective factor, the previous value having been computed during aprevious iteration of the fourth step, the current value beingconstructed by adding, to the previous value, a random variable, saidrandom variable having been drawn according to a predefined probabilitylaw, current values of various particles having been initialized, beforethe first execution of the fourth step, to various initial values, andwherein, during the fourth step, for each particle whose coordinates areupdated with the aid of the displacement law, the value of thecorrective factor in the displacement law is set equal to the currentvalue of the corrective factor that is associated with the particle. 3.The method of claim 2, the corrective factor is one of added andmultiplied by the second measured variable and wherein the variation ofthe standard deviation σ_(ε) of the predefined probability law ismaintained below 10% per second for more than 90% of the time duringwhich the method for locating the device is being used, wherein thevariation of the standard deviation σ_(ε) is given by Σσ_(εk)/T, whereinσ_(εk) is the standard deviation of the predefined probability lawduring the k-th iteration of the fourth step, wherein Σσ_(εk) is the sumof the standard deviations σ_(εk) between the q^(th) iteration and thep^(th) iteration of the fourth step, wherein q is an integer that isless than p, and wherein T is the duration in seconds of the timeinterval which has elapsed between the q^(th) and the p^(th) iterationof the fourth step.
 4. The method of claim 2, wherein the correctivefactor is one of added to and multiplied by the first measured variableand wherein the variation of the standard deviation σ_(α) of thepredefined probability law is maintained below 10° per second for morethan 90% of the time during which the method for locating the device isbeing used, the variation of the standard deviation σ_(α) being given bythe ratio: Σσ_(αk)/T, wherein σ_(αk) is the standard deviation of thepredefined probability law during the k^(th) iteration of the fourthstep, wherein Σσ_(αk) is the sum of the standard deviations σ_(αk)between the q^(th) iteration and the p^(th) iteration of the fourthstep, where q is an integer that is less than p, and wherein T is theduration, in seconds, of the time interval that has elapsed between theq^(th) and the p^(th) iteration of the fourth step.
 5. The method ofclaim 2, further comprising, after having repeatedly executed thesequence of steps, re-sampling the particles, wherein re-sampling theparticles comprises eliminating the particles that are associated withthe lowest weights, automatically generating new particles to replacethe eliminated particles, and assigning a new current value of thecorrective factor to each new particle thus generated, wherein each newvalue depends on one or more of the current values of corrective factorsthat are associated with particles that have not been eliminated andwherein each new value is independent of the current values ofcorrective factors that are associated with particles that have beeneliminated.
 6. The method of claim 1, wherein the predefined constraintscontain coordinates coding the positions and the dimensions of obstaclesthat are impassable to the device in the three-dimensional space, andwherein the fifth step comprises, for each particle: searching for anintersection between a segment that extends between the previousposition and the new position and an impassable obstacle by using thecoordinates of the impassable obstacle that were provided during thefirst step, and decreasing the weight associated with the particle whensuch an intersection exists and, in the converse case, executing one ofthe action chosen in the group composed of the absence of decreasing theweight associated with the particle and increasing the weight associatedwith the particle.
 7. The method of claim 6, wherein the map that wasprovided during the first step contains several distinct zones, eachdistinct zone being associated: with coordinates defining the positionon the map of its periphery and with a list of identifiers of just theimpassable obstacles situated inside the zone, wherein the fifth stepsystematically comprises, for each particle: a first operation followedby a second operation, wherein the first operation comprises identifyingthe zone inside which the particle is situated by comparing the updatedcoordinates of the particle with the peripheries of the zones of themap, and wherein the second operation comprises searching for anintersection between a segment that extends between the previousposition and the new position and solely the impassable obstacles whoseidentifiers are contained in the list associated with the zoneidentified during the first operation.
 8. The method of claim 1, whereinthe map provided during the first step contains at least one zone with afavored direction of displacement, the zone being associated: withcoordinates defining the position, on the map, of the zone's periphery,and with a favored direction of displacement within the zone, whereinthe fifth step comprises, for each particle: detecting the presence ofthe particle inside the zone with the favored direction of displacementby comparing the coordinates of the particle with the periphery of thezone with the favored direction of displacement defined by thecoordinates provided during the first step, when the particle isdetected as being present inside the zone with the favored direction ofdisplacement, increasing the weight of the particle when the angulardeviation between the direction of displacement of the particle from theprevious position to the new position and the favored direction ofdisplacement associated with the zone is equal to 0° or to 180° towithin plus or minus σ_(Y), wherein increasing the weight comprisesincreasing the weight relative to the weights of the other particlessituated inside the same zone and for which the deviation is not equalto 0° or to 180° to within plus or minus σ_(Y), wherein σ_(Y) is apredetermined angular tolerance, and when the particle is detected asbeing outside of the zone with favored direction of displacement,prohibiting the use of the favored direction of displacement associatedwith the zone to update the weight of the particle.
 9. A manufacturecomprising a non-transitory information recording medium that comprisesinstructions for executing the method of claim 1 when the instructionsare executed by said computer.
 10. An apparatus comprising an electronicunit for locating a device displaceable inside a three-dimensionalspace, the electronic unit comprising: a memory containing a map of thethree-dimensional space and predefined constraints on the displacementsof the device in the three-dimensional space and a computer programmedfor: executing a first step, repeating a sequence of steps comprising asecond step, a third step, and a fourth step, and executing a fifthstep, wherein the first step comprises generating several distinctparticles, each particle being associated: with coordinates coding itsposition on the map and with a weight representing the probability thatthe device is situated at the site of the particle, wherein the secondstep comprises receiving measurements representative of the direction ofdisplacement of the device and of the amplitude of the displacement froma previous position of the device, the measurements being carried out bysensors onboard the displaced device, wherein the third step comprisesupdating the coordinates of the position of each particle as a functionof the measurements received and of a predetermined displacement law fordisplacing the particle from a previous position thereof to a newposition thereof in a manner correlated with the measured displacementof the device, wherein the fourth step comprises, for each particle,when the latest displacement of the particle from the previous positionto the new position satisfies the predefined constraints, increasing theweight associated with the particle with respect to the weights of theparticles whose latest displacement fail to satisfy the predefinedconstraints, and wherein the fifth step comprises estimating theposition of the device on the basis of the positions of the particlesand of the weights associated with the particles by allotting, duringthe estimation, more importance to the positions of the particlesassociated with the highest weights, wherein: the map recorded in thememory contains several distinct zones, each distinct zone beingassociated: with coordinates defining the position, on the map, of aperiphery thereof, and a predetermined displacement law from among a setof several different displacement laws, wherein at least two of theseveral distinct zones are associated with different predetermineddisplacement laws, the predetermined displacement law associated with azone having been selected because the predetermined displacement lawmakes it possible to estimate more precisely, on the basis of the samemeasurements received, the direction and the amplitude of thedisplacement of the device when the device is situated inside the zonethan any one of the other displacement laws of the set of severaldifferent displacement laws wherein the different displacement laws aredistinguished from one another by mathematical operations that link thecoordinates of a particle to the measurements received during the secondstep, and wherein the computer is further programmed so as to, duringthe third step and systematically for each particle: identify the zoneinside which the particle is situated by comparing the coordinates ofthe particle with the peripheries of the zones of the map, and then use,for the updating of the coordinates of the particle, just thedisplacement law associated with the identified zone.
 11. The apparatusof claim 10, wherein the device is directly transportable by apedestrian who is moving within the three-dimensional space, the devicecomprising an inertial platform configured to measure physicalquantities representative of the direction of displacement of the deviceand of the amplitude of the displacement, wherein the device comprisesthe electronic unit.
 12. A non-abstract method that comprises making animprovement in the way that computers operate and making an improvementin a technical field, wherein the technical field is that of locating adevice that is displaced inside a three-dimensional space, wherein saidnon-abstract method comprises locating the device, wherein locating thedevice comprises executing a first step, executing a second step,repeatedly executing a third step, a fourth step, and a fifth step, andexecuting a sixth step, wherein said first step comprises providing amap of the three-dimensional space and of predefined constraints on thedisplacements of the device in the three-dimensional space, wherein thesecond step comprises causing an electronic computer to generate severaldistinct particles, wherein each particle is associated with coordinatesthat code the position of the particle on the map and with a weight thatrepresents the probability that the device is situated at the site ofthe particle, wherein the third step comprises receiving measurementsrepresentative of the direction of displacement of the device and of theamplitude of the displacement from a previous position of the device,the measurements being carried out by sensors onboard the displaceddevice, wherein the fourth step comprises updating the coordinates ofthe position of each particle as a function of the measurements receivedduring the third step and of a predetermined displacement law fordisplacing the particle from its previous position P^(i) _(k-1) to a newposition P^(i) _(k) in a manner correlated with the measureddisplacement of the device, wherein the fifth step comprises for eachparticle, when the latest displacement of the particle from the positionP^(i) _(k-1) to the position P^(i) _(k) satisfies the predefinedconstraints, increasing the weight associated with the particle withrespect to the weights of the particles whose latest displacement failsto satisfy the predefined constraints, wherein the sixth step comprisesestimating the position of the device on the basis of the positions ofthe particles and of the weights associated with the particles byallotting, during the estimation, more importance to the positions ofthe particles associated with the highest weights, wherein the map thatwas provided during step the first step contains at least one zone witha favored direction of displacement associated with coordinates definingthe position, on the map, of the zone's periphery, and with a favoreddirection of displacement in the zone, wherein the fifth step furthercomprises, for each particle: detecting the presence of the particleinside the zone with the favored direction of displacement by comparingthe coordinates of the particle with the periphery of the zone with thefavored direction of displacement defined by the coordinates providedduring the first step, and, when the particle is detected as beingpresent inside the zone with the favored direction of displacement,increasing the weight of the particle when the angular deviation betweenthe direction of displacement of the particle from the position P^(i)_(k-1) to the position P^(i) _(k) and the favored direction ofdisplacement associated with the zone is equal to 0° or to 180° towithin plus or minus σ_(Y), wherein increasing the weight is carried outwith respect to the weights of the other particles situated inside thesame zone and for which the deviation is not equal to 0° or to 180° towithin plus or minus σ_(Y), where σ_(Y) is a predetermined angulartolerance, and when the particle is detected as being outside of thezone with the favored direction of displacement, prohibiting the use ofthe favored direction of displacement associated with the zone to updatethe weight of the particle.
 13. The method of claim 12, wherein thedisplacement law comprises: at least one first measured variable whosevalue is dependent on the measurement of the direction of displacementreceived during the third step, a second measured variable whose valueis dependent on the measurement of the amplitude of the displacementreceived during the third step, and a corrective factor of a biascombined by an arithmetical operation with one of the measuredvariables, wherein each particle is also associated with a current valueof the corrective factor, the current value of the corrective factorbeing constructed at each iteration of the fourth step on the basis of aprevious current value of the corrective factor, which was computedduring a previous iteration of the fourth step, to which is added arandom variable drawn according to a predefined probability law, and thecurrent values of various particles being initialized, before the firstexecution of the fourth step, to various initial values, and during thefourth step, for each particle whose coordinates are updated with theaid of the displacement law, the value of the corrective factor in thedisplacement law is taken equal to the corrective factor's current valueassociated with the particle.
 14. The method of claim 13, wherein thecorrective factor is, in the displacement law, added together ormultiplied with the second measured variable and the variation of thestandard deviation aσ_(ε) of the predefined probability law ismaintained below 10% per second for more than 90% of the time of use ofthe method for locating the device, the variation of the standarddeviation σ_(ε) being given by Σσ_(εk)/T, where: σ_(εk) is the standarddeviation of the predefined probability law during the k^(th) iterationof the fourth step, Σσ_(εk) is the sum of the standard deviations σ_(εk)between the q^(th) iteration and the p^(th) iteration of the fourthstep, where q is an integer that is less than p, T is the duration inseconds of the time interval which has elapsed between the q^(th) andthe p^(th) iteration of the fourth step.
 15. The method of claim 13,wherein the corrective factor is, in the displacement law, addedtogether or multiplied with the first measured variable and thevariation of the standard deviation σ_(α) of the predefined probabilitylaw is maintained below 10° per second for more than 90% of the time ofuse of the method for locating the device, the variation of the standarddeviation σ_(α) being given by Σσ_(αk)/T, wherein σ_(αk) is the standarddeviation of the predefined probability law during the k^(th) iterationof the fourth step, wherein Σσ_(αk) is the sum of the standarddeviations σ_(αk) between the q^(th) iteration and the p^(th) iterationof the fourth step, where q is an integer that is less than p, andwherein T is the duration in seconds of the time interval which haselapsed between the q^(th) and the p^(th) iteration of the fourth step.16. The method of claim 13, wherein, after several iterations of thethird through fifth steps, the method comprises a step of re-samplingthe particles during which the particles associated with the lowestweights are eliminated, and new particles are automatically generated toreplace the eliminated particles, a new current value of the correctivefactor being assigned to each new particle, each new value beingdependent on one or more of the corrective factor's current valuesassociated with the particles that have not been eliminated andindependent of the corrective factor's current values associated withthe particles that have been eliminated.
 17. The method of claim 12,wherein, during the first step, the predefined constraints that areprovided contain coordinates that code the positions and the dimensionsof obstacles that are impassable to the device in the three-dimensionalspace, and wherein the fifth step comprises, for each particle,searching for an intersection between the segment [P^(i) _(k-1); P^(i)_(k)] and an impassable obstacle by using the coordinates of theimpassable obstacle that were provided during the first step, decreasingthe weight associated with the particle when such an intersection existsand, in the converse case, executing an action selected from the groupconsisting of refraining from decreasing the weight associated with theparticle and increasing the weight associated with the particle.
 18. Themethod of claim 17, wherein during the first step, the map providedcontains several distinct zones, each distinct zone being associatedwith coordinates defining the position, on the map, of its periphery,and with a list of identifiers of just the impassable obstacles situatedinside the zone, wherein the fifth step comprises, for each particle,identifying the zone inside which the particle is situated by comparingthe updated coordinates of the particle with the peripheries of thezones of the map that are defined by the coordinates provided during thefirst step, and searching for an intersection between the segment [P^(i)_(k-1); P^(i) _(k)] and solely the impassable obstacles whoseidentifiers are contained in the list associated with the zoneidentified during the identification operation.
 19. The method of claim12, wherein the map that was provided during the first step containsseveral distinct zones, each distinct zone being associated withcoordinates defining the position, on the map, of a periphery of thatzone, and with a displacement law from among a set of several differentdisplacement laws, the displacement law associated with a zone making itpossible to estimate, more precisely, on the basis of the samemeasurements received, the direction and the amplitude of thedisplacement of the device when the latter is situated inside the zonethan if any one of the other displacement laws of the set were used,wherein the different displacement laws are distinguished from oneanother by the mathematical operations that link the coordinates of aparticle to the measurements received during the third step, and whereinthe fourth step further comprises, for each particle: identifying thezone inside which the particle is situated by comparing the coordinatesof the particle with the peripheries of the zones of the map, which aredefined by the coordinates provided during the first step, and using,for the updating of the coordinates of the particle, just thedisplacement law associated with the zone identified during theidentification operation.
 20. A tangible and non-transitoryinformation-recording medium, that comprises instructions for causingthe electronic computer to execute the method recited in claim
 12. 21.An apparatus comprising an electronic unit for locating a device that isdisplaceable inside a three-dimensional space, the electronic unitcomprising a memory containing a map of the three-dimensional space andpredefined constraints on the displacements of the device in thethree-dimensional space and an electronic computer whose functionalityhas been improved by programming said electronic computer to carry out afunction that could not have been carried out in the absence of saidprogramming, wherein said electronic computer has been programmed forexecuting a first step, repeatedly executing second, third, and fourthsteps, and executing a fifth step, wherein the first step comprisesgenerating several distinct particles, each particle being associatedwith coordinates coding its position on the map, and with a weightrepresenting the probability that the device is situated at the site ofthe particle, wherein the second step comprises receiving measurementsrepresentative of the direction of displacement of the device and of theamplitude of the displacement from its previous position, themeasurements being carried out by sensors onboard the displaced device,wherein the third step comprises updating the coordinates of theposition of each particle as a function of the measurements received andof a predetermined displacement law for displacing the particle from itsprevious position P^(i) _(k-1) to a new position P^(i) _(k) in a mannercorrelated with the measured displacement of the device, wherein thefourth step comprises, for each particle, when the latest displacementof the particle from the position P^(i) _(k-1) to the position P^(i)_(k) satisfies the predefined constraints, increasing the weightassociated with the particle with respect to the weights of theparticles whose latest displacement infringes these predefinedconstraints, and wherein the fifth step comprises estimating theposition of the device on the basis of the positions of the particlesand of the weights associated with the particles by allotting, duringthe estimation, more importance to the positions of the particlesassociated with the highest weights, wherein the map recorded in thememory contains at least one zone with a favored direction ofdisplacement associated with coordinates defining the position on themap of its periphery, and with a favored direction of displacement inthe zone, and wherein, as part of causing an improvement in computertechnology caused by having programmed said computer to be able to carryout a novel function, the computer is programmed so as to, during thefourth step, and for each particle: detect the presence of the particleinside the zone with favored direction of displacement by comparing thecoordinates of the particle with the periphery of the zone with favoreddirection of displacement defined by the coordinates provided as part ofthe map of the three-dimensional space and of the predefined constraintson the displacements of the device in the three-dimensional space, andthen, when the particle is detected as being present inside the zonewith favored direction of displacement, increase the weight of theparticle when the angular deviation between the direction ofdisplacement of the particle from the position P^(i) _(k-1) to theposition P^(i) _(k) and the favored direction of displacement associatedwith the zone is equal to 0° or to 180° to within plus or minus σ_(Y),wherein increasing the weight is carried out with respect to the weightsof the other particles situated inside the same zone and for which thedeviation is not equal to 0° or to 180° to within plus or minus σ_(Y),where σ_(Y) is a predetermined angular tolerance, and when the particleis detected as being outside of the zone with favored direction ofdisplacement, prohibiting the use of the favored direction ofdisplacement associated with the zone to update the weight of theparticle.
 22. The apparatus of claim 21, further comprising said device,wherein said device is directly transportable by a pedestrian who ismoving in a three-dimensional space, as a result of which the deviceexperiences displacement in the three-dimensional space, wherein thedevice comprises an inertial platform that is able to measure physicalquantities representative of the direction of displacement of the deviceand of the amplitude of the displacement, wherein theelectronic-locating unit is a constituent of the device.